On the local time of the weighted bootstrap and compound empirical processes

Sergio Alvarez-Andrade (1) , Salim Bouzebda (1)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

This article is mainly concerned with the local times of the weighted bootstrap process. We prove a strong approximation theorem for the local time of the weighted bootstrap process by the local time of a Brownian bridge. We consider also the local time of the compound empirical processes that can be seen, asymptotically, as the local time of the convolution of two independent Gaussian processes.

Mots clés: Local time; Brownian bridge; Best approximation; Empirical process; Weighted bootstrap; Strong approximation

Domaines: Statistiques [math.ST]

Sergio Alvarez-Andrade, Salim Bouzebda. On the local time of the weighted bootstrap and compound empirical processes. Stochastic Analysis and Applications, 2015, 33 (4), pp.609-629. ⟨10.1080/07362994.2015.1024854⟩. ⟨hal-01250155⟩